where \(\mathcal {P}_{emb} \in \mathbb {R}^{N\times d_{emb}}\)  is a high-dimensional feature embedding.
During our experiments, we considered other common point cloud embedding methods such as 3D-GCN [1]} demonstrating their power in many category-level pose estimation methods [2]}, [3]}.
During feature aggregation for each point, they use the nearest neighbor algorithm to search nearby points within coordinate space, then calculate new features as a weighted sum of the features within surrounding points. Due to the noisy input \(\hat{D}\)  from Equation (REF ), the nearest neighbor may become unreliable by producing noisy feature embeddings. On the other hand, Pointformer aggregates feature by a transformer-based method. The gradient back-propagates through the whole point cloud. More comparisons and discussions in Section REF  demonstrate that transformer-based embedding methods are more stable than nearest neighbor-based methods when both are trained on noisy depth data.
